You missed single quote sign:
SELECT *
FROM TABLENAME
WHERE DateTime >= '12/04/2011 12:00:00 AM' AND DateTime <= '25/05/2011 3:53:04 AM'
Also, it is recommended to use ISO8601 format YYYY-MM-DDThh:mm:ss.nnn[ Z ], as this one will not depend on your server’s local culture.
SELECT *
FROM TABLENAME
WHERE
DateTime >= '2011-04-12T00:00:00.000' AND
DateTime <= '2011-05-25T03:53:04.000'